Libraries

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import networkx as nx
import warnings
warnings.filterwarnings('ignore')

a. Calculate the correlation matrix

cor_matrix contains the full correlation matrix. The table below shows a snapshot of the first 5 rows.

#reads the csv
stocks = pd.read_csv('asset_prices.csv')
#craetes a correlation matrix
cor_matrix = stocks.iloc[:,1:].corr()
#shows the first 5 rows
cor_matrix.head()

	EOD~BND.11	EOD~DBC.11	EOD~DIA.11	EOD~EEM.11	EOD~EFA.11	EOD~EMB.11	EOD~EPP.11	EOD~EWG.11	EOD~EWI.11	EOD~EWJ.11	...	EOD~VGK.11	EOD~VPL.11	EOD~VXX.11	EOD~XLB.11	EOD~XLE.11	EOD~XLF.11	EOD~XLK.11	EOD~XLU.11	EOD~CSJ.11	EOD~FXF.11
EOD~BND.11	1.000000	-0.822062	0.794479	0.069905	0.114368	0.912854	0.119582	0.099310	-0.482615	0.638039	...	-0.037230	0.536324	-0.900317	0.597031	-0.613705	0.689425	0.845532	0.941027	0.934951	-0.769985
EOD~DBC.11	-0.822062	1.000000	-0.574282	0.349666	0.200079	-0.600426	0.325952	0.228763	0.600429	-0.472528	...	0.333239	-0.215966	0.773717	-0.238640	0.895370	-0.509694	-0.644009	-0.717165	-0.713552	0.870505
EOD~DIA.11	0.794479	-0.574282	1.000000	0.468724	0.563945	0.917934	0.519725	0.568437	-0.070294	0.897045	...	0.412195	0.875397	-0.883305	0.898652	-0.346392	0.975872	0.988677	0.910599	0.917660	-0.657030
EOD~EEM.11	0.069905	0.349666	0.468724	1.000000	0.906563	0.383581	0.968244	0.871560	0.609441	0.553773	...	0.872187	0.788827	-0.162012	0.743330	0.522937	0.488016	0.403966	0.239615	0.227668	0.224999
EOD~EFA.11	0.114368	0.200079	0.563945	0.906563	1.000000	0.412868	0.881808	0.961832	0.722791	0.701312	...	0.975473	0.852729	-0.274274	0.759922	0.333035	0.596364	0.504831	0.291689	0.308123	0.135446

5 rows × 39 columns

#extracts the indices from the correlation matrix, which are the stocks
stocks = cor_matrix.index.values

#Changes from dataframe to matrix, so it is easier to create a graph with networkx
cor_matrix = np.asmatrix(cor_matrix)

b. Create graph

#Crates graph using the data of the correlation matrix
G = nx.from_numpy_matrix(cor_matrix)

#relabels the nodes to match the  stocks names
G = nx.relabel_nodes(G,lambda x: stocks[x])

#Shows the first 5 edges with their corresponding edges
G.edges(data=True)[:5]

[('EOD~IEF.11', 'EOD~IEF.11', {'weight': 1.0}),
 ('EOD~IEF.11', 'EOD~FXB.11', {'weight': -0.8109515006001933}),
 ('EOD~IEF.11', 'EOD~GLD.11', {'weight': -0.0039908434111300085}),
 ('EOD~IEF.11', 'EOD~XLF.11', {'weight': 0.49367913389604445}),
 ('EOD~IEF.11', 'EOD~FXE.11', {'weight': -0.7995281951779287})]

Part 1: The basic graph

#function to create and display networks from the correlatin matrix. 

def create_corr_network_1(G):
    #crates a list for edges and for the weights
    edges,weights = zip(*nx.get_edge_attributes(G,'weight').items())

    #positions
    positions=nx.circular_layout(G)
    
    #Figure size
    plt.figure(figsize=(15,15))

    #draws nodes
    nx.draw_networkx_nodes(G,positions,node_color='#DA70D6',
                           node_size=500,alpha=0.8)
    
    #Styling for labels
    nx.draw_networkx_labels(G, positions, font_size=8, 
                            font_family='sans-serif')
        
    #draws the edges
    nx.draw_networkx_edges(G, positions, edge_list=edges,style='solid')
    
    # displays the graph without axis
    plt.axis('off')
    #saves image
    plt.savefig("part1.png", format="PNG")
    plt.show() 

create_corr_network_1(G)

Part 2: Separating between negative and positive correlations

#function to create and display networks from the correlatin matrix. 

def create_corr_network_2(G, corr_direction):
    ##Creates a copy of the graph
    H = G.copy()
    
    ##Checks all the edges and removes some based on corr_direction
    for stock1, stock2, weight in G.edges_iter(data=True):
        ##if we only want to see the positive correlations we then delete the edges with weight smaller than 0
        if corr_direction == "positive":
            if weight["weight"] <0:
                H.remove_edge(stock1, stock2)
        ##this part runs if the corr_direction is negative and removes edges with weights equal or largen than 0
        else:
            if weight["weight"] >=0:
                H.remove_edge(stock1, stock2)
                
    
    #crates a list for edges and for the weights
    edges,weights = zip(*nx.get_edge_attributes(H,'weight').items())

    #positions
    positions=nx.circular_layout(H)
    
    #Figure size
    plt.figure(figsize=(15,15))

    #draws nodes
    nx.draw_networkx_nodes(H,positions,node_color='#DA70D6',
                           node_size=500,alpha=0.8)
    
    #Styling for labels
    nx.draw_networkx_labels(H, positions, font_size=8, 
                            font_family='sans-serif')
        
    #draws the edges
    nx.draw_networkx_edges(H, positions, edge_list=edges,style='solid')
    
    # displays the graph without axis
    plt.axis('off')
    #saves image
    plt.savefig("part2" + corr_direction + ".png", format="PNG")
    plt.show() 

create_corr_network_2(G,corr_direction="positive")

create_corr_network_2(G,corr_direction="negative")

Part 3: Styling the edges based on their weights

#function to create and display networks from the correlatin matrix. 

def create_corr_network_3(G, corr_direction):
    ##Creates a copy of the graph
    H = G.copy()
    
    ##Checks all the edges and removes some based on corr_direction
    for stock1, stock2, weight in G.edges_iter(data=True):
        ##if we only want to see the positive correlations we then delete the edges with weight smaller than 0
        if corr_direction == "positive":
            if weight["weight"] <0:
                H.remove_edge(stock1, stock2)
        ##this part runs if the corr_direction is negative and removes edges with weights equal or largen than 0
        else:
            if weight["weight"] >=0:
                H.remove_edge(stock1, stock2)
                
    
    #crates a list for edges and for the weights
    edges,weights = zip(*nx.get_edge_attributes(H,'weight').items())
    
    ### increases the value of weights, so that they are more visible in the graph
    weights = tuple([(1+abs(x))**2 for x in weights])

    #positions
    positions=nx.circular_layout(H)
    
    #Figure size
    plt.figure(figsize=(15,15))

    #draws nodes
    nx.draw_networkx_nodes(H,positions,node_color='#DA70D6', 
                           node_size=500,alpha=0.8)
    
    #Styling for labels
    nx.draw_networkx_labels(H, positions, font_size=8, 
                            font_family='sans-serif')
    
    ###edge colors based on weight direction
    if corr_direction == "positive":
        edge_colour = plt.cm.GnBu 
    else:
        edge_colour = plt.cm.PuRd
        
    #draws the edges
    nx.draw_networkx_edges(H, positions, edge_list=edges,style='solid',
                          ###adds width=weights and edge_color = weights 
                          ###so that edges are based on the weight parameter 
                          ###edge_cmap is for the color scale based on the weight
                          ### edge_vmin and edge_vmax assign the min and max weights for the width
                          width=weights, edge_color = weights, edge_cmap = edge_colour,
                          edge_vmin = min(weights), edge_vmax=max(weights))

    # displays the graph without axis
    plt.axis('off')
    #saves image
    plt.savefig("part3" + corr_direction + ".png", format="PNG")
    plt.show() 

create_corr_network_3(G, corr_direction="positive")

create_corr_network_3(G, corr_direction="negative")

Part 4: Filtering edges with a minimum correlation

#function to create and display networks from the correlatin matrix. 

def create_corr_network_4(G, corr_direction, min_correlation):
    ##Creates a copy of the graph
    H = G.copy()
    
    ##Checks all the edges and removes some based on corr_direction
    for stock1, stock2, weight in G.edges_iter(data=True):
        ##if we only want to see the positive correlations we then delete the edges with weight smaller than 0        
        if corr_direction == "positive":
            ####it adds a minimum value for correlation. 
            ####If correlation weaker than the min, then it deletes the edge
            if weight["weight"] <0 or weight["weight"] < min_correlation:
                H.remove_edge(stock1, stock2)
        ##this part runs if the corr_direction is negative and removes edges with weights equal or largen than 0
        else:
            ####it adds a minimum value for correlation. 
            ####If correlation weaker than the min, then it deletes the edge
            if weight["weight"] >=0 or weight["weight"] > min_correlation:
                H.remove_edge(stock1, stock2)
                
    
    #crates a list for edges and for the weights
    edges,weights = zip(*nx.get_edge_attributes(H,'weight').items())
    
    ### increases the value of weights, so that they are more visible in the graph
    weights = tuple([(1+abs(x))**2 for x in weights])

    #positions
    positions=nx.circular_layout(H)
    
    #Figure size
    plt.figure(figsize=(15,15))

    #draws nodes
    nx.draw_networkx_nodes(H,positions,node_color='#DA70D6',
                           node_size=500,alpha=0.8)
    
    #Styling for labels
    nx.draw_networkx_labels(H, positions, font_size=8, 
                            font_family='sans-serif')
    
    ###edge colors based on weight direction
    if corr_direction == "positive":
        edge_colour = plt.cm.GnBu 
    else:
        edge_colour = plt.cm.PuRd
        
    #draws the edges
    nx.draw_networkx_edges(H, positions, edge_list=edges,style='solid',
                          ###adds width=weights and edge_color = weights 
                          ###so that edges are based on the weight parameter 
                          ##edge_cmap is for the color scale based on the weight
                          ### edge_vmin and edge_vmax assign the min and max weights for the width
                          width=weights, edge_color = weights, edge_cmap = edge_colour,
                          edge_vmin = min(weights), edge_vmax=max(weights))

    # displays the graph without axis
    plt.axis('off')
    #saves image
    plt.savefig("part4" + corr_direction + ".png", format="PNG")
    plt.show() 

create_corr_network_4(G, corr_direction="positive", min_correlation = 0.7)

create_corr_network_4(G, corr_direction="negative", min_correlation = -0.7)

Part 5: Styling the nodes based on the number of edges linked (degree)

#function to create and display networks from the correlatin matrix. 

def create_corr_network_5(G, corr_direction, min_correlation):
    ##Creates a copy of the graph
    H = G.copy()
    
    ##Checks all the edges and removes some based on corr_direction
    for stock1, stock2, weight in G.edges_iter(data=True):
        ##if we only want to see the positive correlations we then delete the edges with weight smaller than 0        
        if corr_direction == "positive":
            ####it adds a minimum value for correlation. 
            ####If correlation weaker than the min, then it deletes the edge
            if weight["weight"] <0 or weight["weight"] < min_correlation:
                H.remove_edge(stock1, stock2)
        ##this part runs if the corr_direction is negative and removes edges with weights equal or largen than 0
        else:
            ####it adds a minimum value for correlation. 
            ####If correlation weaker than the min, then it deletes the edge
            if weight["weight"] >=0 or weight["weight"] > min_correlation:
                H.remove_edge(stock1, stock2)
                
    
    #crates a list for edges and for the weights
    edges,weights = zip(*nx.get_edge_attributes(H,'weight').items())
    
    ### increases the value of weights, so that they are more visible in the graph
    weights = tuple([(1+abs(x))**2 for x in weights])
    
    #####calculates the degree of each node
    d = nx.degree(H)
    #####creates list of nodes and a list their degrees that will be used later for their sizes
    nodelist, node_sizes = zip(*d.items())

    #positions
    positions=nx.circular_layout(H)
    
    #Figure size
    plt.figure(figsize=(15,15))

    #draws nodes
    nx.draw_networkx_nodes(H,positions,node_color='#DA70D6',nodelist=nodelist,
                           #####the node size will be now based on its degree
                           node_size=tuple([x**3 for x in node_sizes]),alpha=0.8)
    
    #Styling for labels
    nx.draw_networkx_labels(H, positions, font_size=8, 
                            font_family='sans-serif')
    
    ###edge colors based on weight direction
    if corr_direction == "positive":
        edge_colour = plt.cm.GnBu 
    else:
        edge_colour = plt.cm.PuRd
        
    #draws the edges
    nx.draw_networkx_edges(H, positions, edge_list=edges,style='solid',
                          ###adds width=weights and edge_color = weights 
                          ###so that edges are based on the weight parameter 
                          ###edge_cmap is for the color scale based on the weight
                          ### edge_vmin and edge_vmax assign the min and max weights for the width
                          width=weights, edge_color = weights, edge_cmap = edge_colour,
                          edge_vmin = min(weights), edge_vmax=max(weights))

    # displays the graph without axis
    plt.axis('off')
    #saves image
    plt.savefig("part5" + corr_direction + ".png", format="PNG")
    plt.show() 

create_corr_network_5(G, corr_direction="positive",min_correlation=0.7)

create_corr_network_5(G, corr_direction="negative",min_correlation=-0.7)